Properties

Label 117.1.d
Level 117
Weight 1
Character orbit d
Rep. character \(\chi_{117}(116,\cdot)\)
Character field \(\Q\)
Dimension 0
Newforms 0
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) = \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 117.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 39 \)
Character field: \(\Q\)
Newforms: \( 0 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(117, [\chi])\).

Total New Old
Modular forms 6 0 6
Cusp forms 2 0 2
Eisenstein series 4 0 4

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 0 0

Decomposition of \(S_{1}^{\mathrm{old}}(117, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(117, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)